Brockett earned a bachelor's degree from Peabody College and both a master's degree and doctorate in theater from Stanford University. He taught in Iowa, Indiana, Florida, and California before landing at the University of Texas in 1978, where he took the position of dean of the College of Fine Arts. From 1980 until his retirement in 2006, he was a professor of theater and dance and head of the doctoral program for theater history.
Brockett's many publications include "The Essential Theatre," "Modern Theatre: Realism and Naturalism to the Present" and "The Theatre: An Introduction." His most recent book, "Making the Scene: A History of Stage Design and Technology in Europe and the United States," written with Margaret A. Mitchell and Linda Hardberger, was published in 2010.